https://rifleshooter.com/category/barrel-length-and-velocity/
These guys tested multiple cartridges. I don't think they did 22-250, but they did do 224 Valkyrie and 223/5.56. Not sure how that compares in case capacity to 22-250, but should be getting close. I think that ideally, I would t go below 22" on a '250, but maybe down to 20-21". Shorter than that, I'd probably do 223. I have a 22" 22-250 AI. Don't mind the noise, but shorter will be louder.
On the 243, did you try lighter loads with lighter premium bullets? For example, an 85 gr partition vs 100 gr? Just wondering if you could get the recoil down a bit.